In this Purchase Path the consumer sees the banner impression, 30 days go by, and then they do a search and click on the sponsored link
a) In this attribution rule, you believe that the banner cannot influence and stay relevant to the consumer after 30 days. You believe credit for the conversion should be attributed to the search only.
b) In this attribution rule, you believe the banner is still responsible in part for triggering the search and therefore deserves partial credit for the conversion. The search is also responsible for a percentage of the sale.